After login you will be able to create your own lists of problems.

Problems

Sort

Age

Difficulty

Found: 3

Problems Algebra and arithmetic Word problems Solving problems by inequalities. Going through the cases. Sequences Progressions Arithmetic progression Methods Pigeonhole principle Pigeonhole principle (other) Proof by contradiction

10–12 3.0

Can 100 weights of masses 1, 2, 3, ..., 99, 100 be arranged into 10 piles of different masses so that the following condition is fulfilled: the heavier the pile, the fewer weights in it?

Problem #PRU-34904

Problems Algebra and arithmetic Word problems Solving problems by inequalities. Going through the cases. Methods Pigeonhole principle Pigeonhole principle (other)

11–14 3.0

Is it possible to transport 50 stone blocks, whose masses are equal to \(370, 372,\dots, 468\) kg, from a quarry on seven 3-tonne trucks?

Problem #PRU-35791

Problems Algebra and arithmetic Word problems Solving problems by inequalities. Going through the cases. Methods Extremal principle Algebraic methods Processes and operations

13–14 3.0

Sam and Lena have several chocolates, each weighing not more than 100 grams. No matter how they share these chocolates, one of them will have a total weight of chocolate that does not exceed 100 grams. What is the maximum total weight of all of the chocolates?